When the number of variables grows, the \(\mathsf {vMEM}\)  is somewhat affected by a curse of dimensionality problem. In the context of a factor approach, one should explore the possibility that several variables (e.g. realized volatilities on a large number of assets) share some common component beyond the single nonparametric one suggested by [1]}. On the other hand, the matrix \(\mathbf {\alpha }_1\)  which we envisaged to be full both in theory and in the empirical applications may contain some zeros, and estimating them affects the precision of the estimates. A first attempt was made by [2]} with an adaptive Lasso approach which imposes some penalization on making parameters different from zero at the estimation stage. While promising, there are further refinements in the penalized ML approach, and Lasso is not the only tool available among regularization techniques (cf. ridge–type and/or elastic-net): many of these techniques were successfully introduced in the Vector Autoregression [3]}, [4]}, and, given the similarity of the models could be explored in the context of the \(\mathsf {vMEM}\)  world.
